The Fed Funds rate is the interest rate that depository institutions lend balances (held at the Federal Reserve) to each other overnight. LIBOR is the average overnight offering rate of interest on deposits both inside and outside of the US.

It's important to keep in mind that FF rates only apply to regulated US banks with deposits held in the US, while LIBOR is a market rate for USD deposits held anywhere (no requirement to be US regulated). From a credit risk perspective I think both are virtually the same (I may be wrong), however during "normal times" overnight LIBOR trades a few bps back of the FF rate. I would guess that the spread accounts for the possibility that the Fed provides relief to the FF market in a liquidity crisis and does nothing in the LIBOR market. We saw this recently as the Fed injected liquidity to bring the FF rate down towards its target but did nothing (directly) to lower LIBOR.

At the end of the day you can think of this spread as a measure of liquidity and appetite for taking on interbank credit risk.